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Mirrors > Home > ILE Home > Th. List > nfsum1 | Unicode version |
Description: Bound-variable hypothesis builder for sum. (Contributed by NM, 11-Dec-2005.) (Revised by Mario Carneiro, 13-Jun-2019.) |
Ref | Expression |
---|---|
nfsum1.1 |
Ref | Expression |
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nfsum1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-sumdc 11091 | . 2 DECID | |
2 | nfcv 2258 | . . . . 5 | |
3 | nfsum1.1 | . . . . . . 7 | |
4 | nfcv 2258 | . . . . . . 7 | |
5 | 3, 4 | nfss 3060 | . . . . . 6 |
6 | 3 | nfcri 2252 | . . . . . . . 8 |
7 | 6 | nfdc 1622 | . . . . . . 7 DECID |
8 | 4, 7 | nfralxy 2448 | . . . . . 6 DECID |
9 | nfcv 2258 | . . . . . . . 8 | |
10 | nfcv 2258 | . . . . . . . 8 | |
11 | 3 | nfcri 2252 | . . . . . . . . . 10 |
12 | nfcsb1v 3005 | . . . . . . . . . 10 | |
13 | nfcv 2258 | . . . . . . . . . 10 | |
14 | 11, 12, 13 | nfif 3470 | . . . . . . . . 9 |
15 | 2, 14 | nfmpt 3990 | . . . . . . . 8 |
16 | 9, 10, 15 | nfseq 10196 | . . . . . . 7 |
17 | nfcv 2258 | . . . . . . 7 | |
18 | nfcv 2258 | . . . . . . 7 | |
19 | 16, 17, 18 | nfbr 3944 | . . . . . 6 |
20 | 5, 8, 19 | nf3an 1530 | . . . . 5 DECID |
21 | 2, 20 | nfrexya 2451 | . . . 4 DECID |
22 | nfcv 2258 | . . . . 5 | |
23 | nfcv 2258 | . . . . . . . 8 | |
24 | nfcv 2258 | . . . . . . . 8 | |
25 | 23, 24, 3 | nff1o 5333 | . . . . . . 7 |
26 | nfcv 2258 | . . . . . . . . . 10 | |
27 | nfv 1493 | . . . . . . . . . . . 12 | |
28 | nfcsb1v 3005 | . . . . . . . . . . . 12 | |
29 | 27, 28, 13 | nfif 3470 | . . . . . . . . . . 11 |
30 | 22, 29 | nfmpt 3990 | . . . . . . . . . 10 |
31 | 26, 10, 30 | nfseq 10196 | . . . . . . . . 9 |
32 | 31, 9 | nffv 5399 | . . . . . . . 8 |
33 | 32 | nfeq2 2270 | . . . . . . 7 |
34 | 25, 33 | nfan 1529 | . . . . . 6 |
35 | 34 | nfex 1601 | . . . . 5 |
36 | 22, 35 | nfrexya 2451 | . . . 4 |
37 | 21, 36 | nfor 1538 | . . 3 DECID |
38 | 37 | nfiotaxy 5062 | . 2 DECID |
39 | 1, 38 | nfcxfr 2255 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wo 682 DECID wdc 804 w3a 947 wceq 1316 wex 1453 wcel 1465 wnfc 2245 wral 2393 wrex 2394 csb 2975 wss 3041 cif 3444 class class class wbr 3899 cmpt 3959 cio 5056 wf1o 5092 cfv 5093 (class class class)co 5742 cc0 7588 c1 7589 caddc 7591 cle 7769 cn 8688 cz 9022 cuz 9294 cfz 9758 cseq 10186 cli 11015 csu 11090 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-dc 805 df-3an 949 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-sbc 2883 df-csb 2976 df-un 3045 df-in 3047 df-ss 3054 df-if 3445 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-mpt 3961 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-iota 5058 df-fun 5095 df-fn 5096 df-f 5097 df-f1 5098 df-fo 5099 df-f1o 5100 df-fv 5101 df-ov 5745 df-oprab 5746 df-mpo 5747 df-recs 6170 df-frec 6256 df-seqfrec 10187 df-sumdc 11091 |
This theorem is referenced by: mertenslem2 11273 |
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